Question

Sin 11пи разделить на 3

Answer 1

Sin(11π/3)=sin(4π-π/3)=-sin(π/3)=-0,5

Answer 2

I will try to answer your question using the Bing search results.

The value of sin(11π/3) can be found by using the following steps:

- Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π. This is because the sine function is periodic with a period of 2π, which means that sin(θ) = sin(θ + 2πn) for any integer n. In this case, we have:

sin(11π/3) = sin(11π/3 - 2π) = sin(5π/3)

- Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. To find the reference angle, we can use the formula:

reference angle = π - |θ|

where θ is the given angle in the second or third quadrant, and |θ| is the absolute value of θ. In this case, we have:

reference angle = π - |5π/3| = π - 5π/3 = -2π/3

- Make the expression negative because sine is negative in the fourth quadrant. The sign of the sine function depends on the quadrant of the given angle. In the fourth quadrant, the sine function is negative, so we have:

sin(5π/3) = -sin(reference angle) = -sin(-2π/3)

- Use the special right triangles or the unit circle to find the exact value of the sine function. The special right triangles are the 30-60-90 and the 45-45-90 triangles, which have known ratios of their sides. The unit circle is a circle with radius 1 centered at the origin, which has the coordinates of the terminal points of the angles on the circle. In this case, we can use either method to find the exact value of sin(-2π/3). Using the special right triangles, we can see that -2π/3 is equivalent to -120°, which is the angle opposite to the side with length √3 in the 30-60-90 triangle. Therefore, we have:

sin(-2π/3) = -√3/2

Using the unit circle, we can see that -2π/3 is equivalent to 240°, which is the angle that corresponds to the point (-1/2, -√3/2) on the circle. Therefore, we have:

sin(-2π/3) = -√3/2

- Simplify the expression if possible. In this case, there is no further simplification, so we have:

sin(11π/3) = -√3/2

This is the final answer. You can also check the answer using a calculator or an online tool, such as Mathway, Cuemath, or GeeksforGeeks. They will give you the same result, or a decimal approximation, such as -0.86602540. I hope this helps you understand how to find the value of sin(11π/3).